What is the integral of (1+tan(x))/(x+ln|sec(x)|) ?

The integral of (1+tan(x))/(x+ln|sec(x)|) is ln|x+ln|sec(x)||+C

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integral of (1+tan(x))/(x+ln|sec(x)|)

\int \frac{1 + tan ( x )}{x + ln ∣ sec ( x ) ∣} d x

ln ∣ x + ln ∣ sec (x) ∣ ∣ + C

Solution steps

\int \frac{1 + tan ( x )}{x + ln ∣ sec ( x ) ∣} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x + ln ∣ sec (x) ∣

= ln ∣ x + ln ∣ sec (x) ∣ ∣

Add a constant to the solution

= ln ∣ x + ln ∣ sec (x) ∣ ∣ + C

\frac{d}{d x} (x 4 + 3 x^{3})

\frac{d}{d x} (3 sin (5 x))

x \to \infty lim ((\frac{1}{3})^{x + 2} + 4)

\frac{4 s}{( 4 s ^{2} + 1 )}

\frac{d}{d x} (3 + cos (x))

What is the integral of (1+tan(x))/(x+ln|sec(x)|) ?
The integral of (1+tan(x))/(x+ln|sec(x)|) is ln|x+ln|sec(x)||+C